$\dfrac{ -7s - 2t }{ 5 } = \dfrac{ 9s + 4u }{ -10 }$ Solve for $s$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -7s - 2t }{ {5} } = \dfrac{ 9s + 4u }{ -10 }$ ${5} \cdot \dfrac{ -7s - 2t }{ {5} } = {5} \cdot \dfrac{ 9s + 4u }{ -10 }$ $-7s - 2t = {5} \cdot \dfrac { 9s + 4u }{ -10 }$ Multiply both sides by the right denominator. $-7s - 2t = 5 \cdot \dfrac{ 9s + 4u }{ -{10} }$ $-{10} \cdot \left( -7s - 2t \right) = -{10} \cdot 5 \cdot \dfrac{ 9s + 4u }{ -{10} }$ $-{10} \cdot \left( -7s - 2t \right) = 5 \cdot \left( 9s + 4u \right)$ Distribute both sides $-{10} \cdot \left( -7s - 2t \right) = {5} \cdot \left( 9s + 4u \right)$ ${70}s + {20}t = {45}s + {20}u$ Combine $s$ terms on the left. ${70s} + 20t = {45s} + 20u$ ${25s} + 20t = 20u$ Move the $t$ term to the right. $25s + {20t} = 20u$ $25s = 20u - {20t}$ Isolate $s$ by dividing both sides by its coefficient. ${25}s = 20u - 20t$ $s = \dfrac{ 20u - 20t }{ {25} }$ All of these terms are divisible by $5$ $s = \dfrac{ {4}u - {4}t }{ {5} }$